Abstract
The scalable solution to constrained combinatorial problems in high dimensions can address many challenges encountered in scientific and engineering disciplines. Inspired by the use of graph neural networks for quadratic-cost combinatorial optimization problems, Heydaribeni and colleagues proposed HypOp, which aims to efficiently solve general problems with higher-order constraints by leveraging hypergraph neural networks to extend previous algorithms to arbitrary cost functions. It incorporates a distributed training architecture to handle larger-scale tasks efficiently. Here we reproduce the primary experiments of HypOp and examine its robustness with respect to the number of graphics processing units, distributed partitioning strategies and fine-tuning methods. We also assess its transferability by applying it to the maximum clique problem and the quadratic assignment problem. The results validate the reusability of HypOp across diverse application scenarios. Furthermore, we provide guidelines offering practical insights for effectively applying it to multiple combinatorial optimization problems.
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Data availability
All data used in the reproduction experiment and robustness evaluation experiment were generated following the methodology outlined in ref. 7. The datasets, including hypergraph data, MaxCut data, MIS data, MaxClique data and QAPLIB data, are available via GitHub at https://github.com/AhauBioinformatics/HypOp_Reuse/tree/main/data (ref. 31). Source data are provided with this paper.
Code availability
The original HypOp code is available via Code Ocean at https://doi.org/10.24433/CO.4804643.v1 (ref. 8). Our modified HypOp version with changes is available via GitHub at https://github.com/AhauBioinformatics/HypOp_Reuse (ref. 31).
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (grant nos. 62472005, 62102004) (Z.Y.), the Anhui Province Excellent Young Teacher Training Project (grant no. YQYB2024007) (Z.Y.) and the National Undergraduate Innovation and Entrepreneurship Training Programme Project (grant no. 202510364005) (J.G.).
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Z.Y. and J.X. conceived of and supervised the project. X.L., J.G. and Z.Y. designed the computational experiments and data analyses. X.L., W.X., B.W. and K.C. prepared the data. X.L., J.G., P.W. and W.X. implemented the methods, conducted the experiments and performed the data analyses. X.L., J.G. and Z.Y. wrote the paper.
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Nature Machine Intelligence thanks Martin Schuetz, Petar Veličković and Haoyu Wang for their contribution to the peer review of this work.
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Extended data
Extended Data Fig. 1 Transfer Learning.
a, b: Transfer learning using HypOp from Graph MaxCut to MIS on synthetic random regular graphs. c, d: Transfer learning using HypOp from Hypergraph MaxCut to Hypergraph MinCut on synthetic random hypergraphs.
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Li, X., Gui, J., Xue, W. et al. Reusability report: A distributed strategy for solving combinatorial optimization problems with hypergraph neural networks. Nat Mach Intell 7, 1870–1878 (2025). https://doi.org/10.1038/s42256-025-01141-4
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DOI: https://doi.org/10.1038/s42256-025-01141-4
